Evaluate SS Pods where È CM,y,z) = 5 zex, sy, 2-yz?> s is the where s...
How to solve it?
Let F =< -2, x, y2 >. Find S Ss curlF.nds, where S is the paraboloid z = x2 + y?, OSz54.
using this formula
2. Evaluate the surface integral F. dS, where F(x, y, z) = xi+yj+zk is taken over the paraboloid z=1 – x2 - y2, z > 0. SA errom bove de SS (-P (- Puerto Q + R) dA dy
Let z=5 where x, y, z E R. Prove that z? +z2+z?>
F(x,y,z) =< P, Q, R >=< xz, yz, 2z2 > S: Bounded by z = 1 – x2 - y2 and z = 0) Flux =SS F ñds S (8a) Find the Flux of the vector field F through this closed surface.
2. (35pt)Evaluate SS 3xy²dA, where R is the region bounded by the graphs of y = -x and y = x2, x > 0 and the graph of x = = 1. R
14. Let S be the cylinder {(x, y, z)| x2 +22 = 25,0 SY <2}. Orient S by the outward pointing normal n = (x/5,0,2/5). Evaluate Fds, where F(x, y, z) = (x – 2, y, x + 2). Hint: The area of a cylinder of radius r and height h is 2nrh.
step by step please, thank
you
(2) Use Stokes' Theorem to evaluate the integral F.dr, where F(x, y, z) =< -Y, I, z > and where S is the upper hemispherical surface defined by z = v1- 2 - y2. The boundary of S is the curve C defined by Cos (t) y= sin (t) 0t 27 Z=0
Evaluate the surface integral lis(r,y,z) (x, y, z) ds where f(x, y, z) = x + y + z and o is the is the surface of the cube defined by the inequalities 0 < x < 5,0 Sy < 5 and 0 <3 < 5. [Hint: integrate over each face separately.] 1 f(x, y, z) ds =
where 7 is the region defined by >0, y >0, >0, r+y+z<3.
(2) Suppose V F = (ex: -2yre?",0). Compute SS (V F). ds, where is the upper unit hemisphere r? + y + z2 = 1, 2 > 0. (Hint: Can you use result of 1 and a more convenient surface over which to integrate?)